On the other hand, if we consider the pencil \(\widehat{L}_s(\lambda )\)  in (REF ), then Theorem  proves that \(L_s(\lambda )\)  is strictly equivalent to \(\mbox{${\rm diag}(0,\widehat{L}_s(\lambda ))$}\) . Combining the results above, we see that \(\widehat{L}_s(\lambda )\)  and \(\mbox{${\rm diag}(I_r,P(\lambda ))$}\)  have the same normal rank and the same finite eigenvalues and partial multiplicities, which implies that \(\widehat{L}_s(\lambda )\)  and \(\mbox{${\rm diag}(I_r,P(\lambda ))$}\)  are unimodularly equivalent [1]} and, therefore, that \(\widehat{L}_s(\lambda )\)  is a GLR-linearization of \(P(\lambda )\) . This is a particular instance of the result mentioned in Section REF  that any minimal linear polynomial system matrix of \(P(\lambda )\)  is a GLR-linearization of \(P(\lambda )\) .
